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arXiv · hep-th/9406098

Non-standard quantum so(2,2) and beyond

A. Ballesteros·F. J. Herranz·M. A. del Olmo·M. Santander
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Abstract

A new "non-standard" quantization of the universal enveloping algebra of the split (natural) real form $so(2,2)$ of $D_2$ is presented. Some (classical) graded contractions of $so(2,2)$ associated to a $Z_2 \times Z_2$ grading are studied, and the automorphisms defining this grading are generalized to the quantum case, thus providing quantum contractions of this algebra. This produces a new family of "non-standard" quantum algebras. Some of these algebras can be realized as (2+1) kinematical algebras; we explicitly introduce a new deformation of Poincaré algebra, which is naturally linked to the null plane basis. Another realization of these quantum algebras as deformations of the conformal algebras for the two-dimensional Euclidean, Galilei and Minkowski spaces is given, and its new properties are emphasized.

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A. Ballesteros, F. J. Herranz, M. A. del Olmo, M. Santander. 1999-02-22. Non-standard quantum so(2,2) and beyond. https://doi.org/10.1088/0305-4470%2F28%2F4%2F018

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